Wireless communication technology has advanced to its present state of the art in part due to digital quadrature modulation (DQM, the acronym also referring also to digital quadrature modulators) and direct digital modulation techniques. Such systems may employ radio-frequency digital-to-analog converters (RFDAC) or digital power amplifiers (DPA) that generate an output voltage or current in accordance a number of current cells that are active therein. Current cell mismatch and intermodulation distortion (IMD) can impact both amplitude and phase at the output of a DPA.
FIG. 1A is an illustration of an exemplary modulation constellation 100, which, merely for purposes of explanation, is an 8-symbol phase-shift keying (PSK) modulator constellation. Constellation 100 includes 8 modulation symbols 120a-120h, representatively referred to herein as symbol(s) 120. Distortion in a DPA can cause a symbol 120b′ to be generated that is removed from its specified symbol state, i.e., at symbol 120b, by an amplitude error AD and a phase error φD. Errors AD and φD can manifest themselves in erroneous decisions at a receiver to which symbols 120 are transmitted by the DPA.
The values of AD and φD can be determined from, for example, a modulation error vector 130 measurement by suitable test equipment. By making a suitable number of such measurements, an amplitude modulation (AM) to AM (AMAM) distortion profile and an AM to phase modulation (AMPM) distortion profile can be obtained. From such AMAM and AMPM distortion profiles, corresponding AMAM and AMPM predistortion profiles can be determined, such as by a suitable functional inversion of the AMAM and AMPM distortion profiles. An example of an AMAM predistortion profile is illustrated in FIG. 1B by AMAM predistortion curve 150 in graph 140 and an example of an AMPM predistortion profile is illustrated in FIG. 1B by AMPM predistortion curve 170 in graph 160. Line 145 in graph 140 illustrates a target amplitude linearization in the DPA to be achieved by applying AMAM predistortion according to AMAM predistortion curve 150 and line 165 in graph 160 illustrates a target phase linearization to be achieved by applying AMPM predistortion according to AMPM predistortion curve 170. Applying AMAM predistortion to data provided to a DPA can reduce or even eliminate the amplitude error AD and, likewise applying AMPM predistortion to the DPA can reduce or eliminate phase error φD.
In DQM transmitters, separate in-phase (I) and quadrature (Q) data channels may be constructed and parallel processing may be performed in the I and Q data channels from the modulator at which they are generated to the DPA circuit that upconverts I and Q data into an output signal. One technique for applying both AMAM and AMPM predistortion is by converting Cartesian I and Q data into a polar representation thereof, i.e.,
            A      =                                    i            2                    +                      q            2                                ,                  for        ⁢                                  ⁢        I            =                        i          ⁢                                          ⁢          and          ⁢                                          ⁢          Q                =        q              ,    and        ϕ    =                  arg        ⁡                  (                      i            ,            q                    )                    =              {                                                                              arctan                  ⁡                                      (                                          q                      /                      i                                        )                                                  ,                                                                    i                >                0                                                                                                                              π                    /                    2                                    -                                      arctan                    ⁡                                          (                                              i                        /                        q                                            )                                                                      ,                                                                    q                >                0                                                                                                                                                    -                      π                                        /                    2                                    -                                      arctan                    ⁡                                          (                                              i                        /                        q                                            )                                                                      ,                                                                    q                <                0                                                                                                          π                  +                                      arctan                    ⁡                                          (                                              q                        /                        i                                            )                                                                      ,                                                                                      i                  <                  0                                ,                                  q                  ≥                  0                                                                                                                                              -                    π                                    +                                      arctan                    ⁡                                          (                                              q                        /                        i                                            )                                                                      ,                                                                                      i                  <                  0                                ,                                  q                  <                  0                                                                                                        Undefined                ,                                                                                      i                  =                  0                                ,                                  q                  =                  0                                                                        
Subsequent to such conversion, the predistortion can be achieved by applying amplitude A and phase φ corrections, e.g., APD=A+AAMAM and φPD=φ+φAMPM, where APD and φPD are the predistorted amplitude and phase, respectively, of the data to be provided to the DPA, AAMAM is the AMAM predistortion value, which can be positive or negative, and φAMPM is the AMPM predistortion value, which also may be positive or negative. However, in DQM systems, the APD and φPD values must be converted back into Cartesian representations I and Q, requiring additional hardware and a longer critical path. Applying both AMAM and AMPM directly to Cartesian I and Q data is challenging in that changing the I and Q values separately to effect AMAM predistortion can cause an additional phase rotation that must be compensated for in AMPM predistortion or by a suitable phase rotation technique. Likewise, applying AMPM on separate I and Q values produces additional compansion, i.e., compression or expansion in amplitude, which must be compensated for by AMAM predistortion.
Given the state of the current art, the need is apparent for a technique by which Cartesian AMAM and AMPM predistortion can be applied to linearize a DPA.